Stochastic models for structured populations scaling limits and long time behavior / [electronic resource] :

• 作者： Bansaye, Vincent.
• 其他作者：
  • Meleard, Sylvie.
  • SpringerLink (Online service)
• 其他題名：
  • Mathematical Biosciences Institute lecture series,
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： Mathematical Biosciences Institute lecture series,1.4
• 主題： Stochastic processes--Mathematical models , Mathematics , Probability Theory and Stochastic Processes. , Genetics and Population Dynamics , Theoretical Ecology/Statistics.
• ISBN： 9783319217116 (electronic bk.) 、 9783319217109 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: Introduction -- Discrete Monotype Population Models and One-dimensional Stochastic Differential Equations -- Birth and Death Processes -- Scaling Limits for Birth and Death Processes -- Continuous State Branching Processes -- Feller Diffusion with Random Catastrophes -- Structured Populations and Measure-valued Stochastic Differential Equations -- Population Point Measure Processes -- Scaling limits for the individual-based process -- Splitting Feller Diffusion for Cell Division with Parasite Infection -- Markov Processes along Continuous Time Galton-Watson Trees -- Appendix.
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• 摘要註: In this contribution, several probabilistic tools to study population dynamics are developed. The focus is on scaling limits of qualitatively different stochastic individual based models and the long time behavior of some classes of limiting processes. Structured population dynamics are modeled by measure-valued processes describing the individual behaviors and taking into account the demographic and mutational parameters, and possible interactions between individuals. Many quantitative parameters appear in these models and several relevant normalizations are considered, leading to infinite-dimensional deterministic or stochastic large-population approximations. Biologically relevant questions are considered, such as extinction criteria, the effect of large birth events, the impact of environmental catastrophes, the mutation-selection trade-off, recovery criteria in parasite infections, genealogical properties of a sample of individuals. These notes originated from a lecture series on Structured Population Dynamics at Ecole polytechnique (France) Vincent Bansaye and Sylvie Meleard are Professors at Ecole Polytechnique (France) They are a specialists of branching processes and random particle systems in biology. Most of their research concerns the applications of probability to biodiversity, ecology and evolution.
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